Create fixed length non-repeating permutation of larger set

Question

I know this topic is much discussed but I can\'t seem to find any implementation that fits my needs.

I have the following set of characters:

a b c

Answer 1

If you only need one element at a time, you can save on memory by generating each element individually.

If we wanted to generate a random string in your set of expected outputs, we could use this algorithm:

Given a set of characters S, and a desired output length K:
  While the output has less than K characters:
    Pick a random number P between 1 and |S|.
    Append the P'th character to the output.
    Remove the P'th character from S.

where |S| is the current number of elements in S.

We can actually encode this sequence of choices into an integer. One way to do that is to change the algorithm as such:

Given a set of characters S, and a desired output length K:
  Let I = 0.
  While the output has less than K characters:
    I = I * (|S| + 1).
    Pick a random number P between 1 and the number of elements in S.
    I = I + P.
    Append the P'th character to the output.
    Remove the P'th character from S.

After running this algorithm, the value I will uniquely encode this particular sequence of choices. It basically encodes this as a mixed-radix number; one digit uses base N, the next uses N-1, and so on until the last digit which is base N-K+1 (N being the number of letters in the input).

Naturally, we can also decode this again, and in PHP, that would be something like this:

// Returns the total number of $count-length strings generatable from $letters.
function getPermCount($letters, $count)
{
  $result = 1;
  // k characters from a set of n has n!/(n-k)! possible combinations
  for($i = strlen($letters) - $count + 1; $i <= strlen($letters); $i++) {
    $result *= $i;
  }
  return $result;
}

// Decodes $index to a $count-length string from $letters, no repeat chars.
function getPerm($letters, $count, $index)
{
  $result = '';
  for($i = 0; $i < $count; $i++)
  {
    $pos = $index % strlen($letters);
    $result .= $letters[$pos];
    $index = ($index-$pos)/strlen($letters);
    $letters = substr($letters, 0, $pos) . substr($letters, $pos+1);
  }
  return $result;
}

(Note that for simplicity, this particular decoding algorithm does not correspond exactly to the encoding algorithm I previously described, but maintains the desirable property of a given $index mapping to a unique result.)

To use this code, you would do something like this:

$letters = 'abcd';
echo '2 letters from 4:
';
for($i = 0; $i < getPermCount($letters, 2); $i++)
  echo getPerm($letters, 2, $i).'
';

echo '
3 letters from 4:
';
for($i = 0; $i < getPermCount($letters, 3); $i++)
  echo getPerm($letters, 3, $i).'
';
?>